मराठी

If (N + 1)! = 90 [(N − 1)!], Find N. - Mathematics

Advertisements
Advertisements

प्रश्न

If (n + 1)! = 90 [(n − 1)!], find n.

Advertisements

उत्तर

(n + 1)! = 90 [(n − 1)!]

\[\Rightarrow\](n + 1)\[\times\](n)\[\times\](n−1)! = 90[(n − 1)!]
\[\Rightarrow\](+ 1)\[\times\](n) = 90
\[\Rightarrow\](n + 1)\[\times\](n) = 10\[\times\] 9
On comparing, we get:
n = 9

 

shaalaa.com
Factorial N (N!) Permutations and Combinations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.1 [पृष्ठ ४]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.1 | Q 8 | पृष्ठ ४

संबंधित प्रश्‍न

Convert the following products into factorials:

5 · 6 · 7 · 8 · 9 · 10


Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18


Convert the following products into factorials: 

(n + 1) (n + 2) (n + 3) ... (2n)


If (n + 2)! = 60 [(n − 1)!], find n. 


Prove that:

\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]


If P (9, r) = 3024, find r.


If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.


If P (n, 5) : P (n, 3) = 2 : 1, find n.


If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.


How many three-digit numbers are there, with no digit repeated?


In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?


All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels occupy only the odd places?


How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the letters P and I respectively occupy first and last place?


How many permutations can be formed by the letters of the word, 'VOWELS', when

there is no restriction on letters?


m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]


Find the number of words formed by permuting all the letters of the following words:

RUSSIA


Find the number of words formed by permuting all the letters of the following words:
SERIES


Find the number of words formed by permuting all the letters of the following words:
EXERCISES


Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.


How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?


How many different numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.


How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?


How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?


How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?


In how many ways can the letters of the word ASSASSINATION be arranged so that all the S's are together?


Evaluate

\[^ {20}{}{C}_5 + \sum^5_{r = 2} {}^{25 - r} C_4\]

There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.


How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if (i) 4 letters are used at a time 


How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if  all letters are used at a time 


How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?


Find the number of permutations of n different things taken r at a time such that two specified things occur together?


Write the number of diagonals of an n-sided polygon.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×